docs: def _Stichlmair_flood_f_and_jac(inputs, Vl, rhog, rhol, mug, voidage, 
                                  specific_area, C1, C2, C3, H):
      '''Internal function which calculates the errors of the two Stichlmair
      objective functions, and their jacobian.
      
      Derived using SymPy on the main flooding function.
      '''
      Vg, dP_irr = float(inputs[0]), float(inputs[1])
      x0 = 1.0/H
      x1 = Vg*Vg
      x2 = voidage**(-4.65)
      x3 = specific_area*x2
      x4 = Vl*Vl*x3/g
      x5 = x4**0.333333333333333
      x6 = dP_irr*dP_irr
      x7 = H*H
      x8 = 1.0/x7
      x9 = g*g
      x10 = 1.0/x9
      x11 = rhol*rhol
      x12 = 1.0/x11
      x13 = x5*(20.0*x10*x12*x6*x8 + 1.0)
      x14 = 0.555*x13
      x15 = (voidage/(voidage - x14))**4.65
      x16 = 1.0/Vg
      x17 = 1.0/rhog
      x18 = voidage - 1.0
      x19 = 1.0/x18
      x20 = C1*mug*specific_area*x16*x17*x19
      x21 = 2.44948974278318*C2
      x22 = Vg*rhog/(mug*specific_area)
      x23 = x21*(-x18*x22)**-0.5
      x24 = 6.0*C3 - x20 + x23
      x25 = 1.0 - voidage 
      x26 = x14 + x25
      x27 = -x19*x26
      x28 = 2.0*C1*mug*specific_area*x16*x17/x25 + x21*(x22*x25)**-0.5
      x29 = 1.0/x24
      x30 = x28*x29
      x31 = x27**(-0.166666666666667*x30 + 0.666666666666667)
      x32 = x11*x7*x9
      x33 = 200.0*voidage
      x34 = 111.0*x13
      x35 = x33 - x34
      x36 = 1.0/x35
      x37 = -x33 + x34 + 200.0
      x38 = 1.0/x37
      x39 = 2.0*x20
      x40 = -4.0*x20 + x23 + x29*(-x23 + x39)*(x23 - x39)
      x41 = dP_irr*rhog*specific_area*x0*x1*x10*x12*x15*x2*x24*x31
      x42 = dP_irr*x10*x12*x4**0.666666666666667*x8
      
      F1, F2, dF1_dVg, dF2_dVg, dF1_dP_irr, dF2_dP_irr = (
              -dP_irr*x0 + 0.0208333333333333*rhog*specific_area*x1*x15*x2*x24*x31,
               x32/x6 - 20646.0*x36*x5 - x38*x5*(2960.0 - 740.0*x28*x29),
               0.00173611111111111*Vg*rhog*x15*x3*x31*(144.0*C3 - 12.0*x20 + 18.0*x23 + x40*log(x27)),
               x0*(430.125*x36*x41*x5 - 15.4166666666667*x38*x41*x5*(x30 - 4.0) - 1.0),
               -1.85*x16*x29*x40*x5/x26,
               3285600.0*x42*(-x30 + 4.0)*x38*x38- 91668240.0*x42*x36*x36 - 2.0*x32/(dP_irr*x6))
      
      return [F1, F2], [[dF1_dVg, dF2_dVg], [dF1_dP_irr, dF2_dP_irr]]